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The Paris Meridian Arc Length and Definition of the Metre

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The Paris Meridian Arc Length and Definition of the Metre Professional paper | Received: 21 -04-201 2 | Accepted: 04-1 2-201 3 The Paris Meridian Arc Length and Definition of the Metre Miljenko SOLARIĆ and Nikola SOLARIĆ University of Zagreb, Faculty of Geodesy, Kačićeva 26, 1 0000 Zagreb, Croatia [email protected], [email protected] Abstract: Pierre François-André Méchain and Jean-Baptiste Joseph Delambre participated in measuring the Paris meridian arc length in order to determine the length of the metre. Jean-Baptiste Biot and François Dominique Jean Arago worked on extending the meridian at a later date. Keywords: meridian arc length, Paris meridian, surveying, trigonometric chain, definition of length in the International System of Units, metre 1 Introduction 2 The Survey of the Paris Meridian Arc Length in Order to Define the Length of the Metre General economic growth in France during the 18th century resulted in the rapid development of trade, in- Pierre François-André Méchain (1744–1804) (Fig. 1) dustry and navigation and the need to introduce unique came from a poor family. He wanted to become an ar- units of measurement. Thus, the French Royal Academy chitect, but he was also very interested in astronomy. of Sciences started a project to establish new units of His mathematical ability was noted early. Education at measurement in 1791, as they were being demanded by L’École Nationale des Ponts et Chaussées in Paris was ex- all larger commerce networks in France and throughout pensive, so he had to leave and tutored two boys from the world. The intention was to define a new unit of len- noble families near Paris, which enabled him to pur- gth called the metre, representing one ten-millionth of chase some good astronomical instruments and pursue the meridian arc from the North Pole to the Equator. The his hobby. However, his father lost a court case and Mé- French wanted to define the metre using the meridian chain had to agree to sell his instruments in order to passing through Paris, but there were several other pro- settle the family’s debt. His instruments were bought by posals. In addition, new units of measurement were to Jérõme Lalande, who was impressed with Méchain’s be introduced in the decimal system in order to facilitate abilities. Méchain spent next years producing maps and trade. At first, the task of measuring the Paris meridian searching for comets. He produced some of maps for arc length was entrusted to Cassini IV, Legendre and Mé- military use in Germany and Italy. Afterwards, he helped chain. Subsequently, however, the Constituent Assembly Cassini IV determine the distance between the Green- of France charged François-André Méchain and Jean- wich and Paris observatories using a trigonometric net- Baptiste Joseph Delambre in 1795 with the task of sur- work. At first, he used old instruments, and later, a veying the section of the Paris meridian between Dun- repeating circle. He soon became known as the most kirk and Barcelona (URL5). Conducting the survey precise observer. In addition to comets, he recorded 29 proved to be much more dangerous than the young sci- nebulae and became a member of the Royal Academy of entists had thought, as it coincided with the difficult Sciences (URL3). times of the French Revolution. Therefore, we are going In 1791, the Committee for Weights and Measures to describe their work and the problems they faced. proposed to the National Assembly that Méchain and KiG No. 20, Vol. 1 2, 201 3 1 8 Stručni rad | Primljeno: 21 -04-201 2 | Prihvaćeno: 04-1 2-201 3 Duljina luka Pariškog meridijana i definicija metra Miljenko SOLARIĆ i Nikola SOLARIĆ Sveučilište u Zagrebu, Geodetski fakultet, Kačićeva 26, 1 0000 Zagreb [email protected], [email protected] Sažetak: Na točnoj izmjeri duljine luka Pariškog meridijana za potrebe određivanja duljine metra sudjelovali su Pierre François-André Méchain i Jean-Baptiste Joseph Delambre. Poslije su na njegovu produženju radili Jean-Baptiste Biot i François Dominique Jean Arago. Ključne riječi: duljina luka meridijana, Pariški meridijan, izmjera, trigonometrijski lanac, definicija duljine međunarodnoga sustava jedinica mjera, metar 1 . Uvod 2. Izmjera duljine luka Pariškog meridijana za potrebe definiranja duljine metra Opći ekonomski rast Francuske očitovao se u brzom usponu trgovine, industrije i pomorstva tijekom 18. sto- Pierre François-André Méchain (1744–1804) (sl. 1) ljeća i tada dolazi do potrebe uvođenja jedinstvenih potjecao je iz siromašne obitelji. Želio je postati arhitekt, mjernih jedinica. Tako je Kraljevska akademija znanosti ali imao je i posebice velik interes za astronomiju. Nje- u Francuskoj 1791. godine postavila projekt uspostave gova sposobnost za matematiku bila je odmah uočena. novih mjernih jedinica jer su to tražile sve veće trgovač- Studiranje na École Nationale des Ponts et chaussées u ke veze u Francuskoj i u svijetu. Željelo se definirati novu Parizu bilo je skupo pa je morao prekinuti studij i podu- jedinicu za duljinu nazvanu metar kao 10-milijunti dio čavati dva dječaka iz plemićkih obitelji u blizini Pariza. duljine luka meridijana od sjevernog pola do ekvatora. Tako je mogao kupiti neke astronomske instrumente Francuzi su željeli da metar bude definiran s pomoću dobre kvalitete i nastaviti svoj hobi. Međutim, kad je meridijana koji prolazi kroz Pariz, no bilo je i više drugih njegov otac izgubio parnicu, morao je prodati svoje prijedloga. Osim toga nastojalo se uvesti nove jedinice instrumente i isplatiti obiteljski dug. Njegove instru- mjera u decimalnom sustavu jer je na taj način bila olak- mente kupio je Jérõme Lalande, koji je bio impresioniran šana trgovina. Na početku su za taj zadatak izmjere Méchainovom sposobnošću. Sljedećih nekoliko godina duljine luka Pariškoga meridijana bili zaduženi Cassini izrađivao je karte i tražio komete. Neke od tih karata iz- IV., Legendre i Méchain. Međutim, poslije je Ustavotvor- radio je za vojsku u Njemačkoj i Italiji. Zatim je pomagao na skupština Francuske 1795. godine zadužila Pierrea Cassiniju IV. 1787. godine na određivanju točne udalje- François-Andréa Méchaina i Jean-Baptistea Josepha nosti između opservatorija u Greenwichu i Parizu s po- Delambrea da točno izmjere dio luka Pariškog meridija- moću trigonometrijske mreže. Na početku je mjerio na od Dunkerquea do Barcelone (URL5). Pri izvođenju te starim instrumentima, a poslije Bordinim repeticijskim izmjere pokazalo se da je to puno opasniji pothvat nego krugom. Ubrzo je stekao ugled najpreciznijeg opažača. što su mislili mladi znanstvenici. Naime, to je bilo teško Osim kometa registrirao je i 29 maglica pa je bio izabran i vrijeme kad se u Francuskoj dogodila revolucija. Zato u Kraljevsku akademiju znanosti (URL3). ćemo opisati njihov rad i probleme s kojima su se susreli. Povjerenstvo za utege i mjere predložilo je 1791. KiG Br. 20, Vol. 1 2, 201 3 1 9 SOLARIĆ, M. AND SOLARIĆ, N.: THE PARIS MERIDIAN ARC LENGTH AND DEFINITION OF THE METRE Figure 1 . Pierre Méchain (1 744-1 804) (URL4) Figure 2. Jean-Baptiste Joseph Delambre (1 749-1 822) (URL2) Slika 1 . Pierre Méchain (1 744–1 804) (URL4) Slika 2. Jean-Baptiste Joseph Delambre (1 749–1 822) (URL2) Delambre survey the trigonometric chain between between the latitudes of the first and last point on the Dunkirk and Barcelona, in order to determine the meridian arc was very important and required great length of the metre. The trigonometric chain was di- care. That was a reason for him to be worried. vided into two parts. Delambre was to survey the north- The situation in France was chaotic, so Méchain fol- ern section from the belfry in Dunkirk (Fig. 3) to Rodez lowed his friend’s advice and went from Spain to Genova Cathedral, a distance of 742.7 km, which had been sur- in neutral Italy, where he was informed that the meridi- veyed by Cassini de Thury prior to 1740. Méchain was to an project had been cancelled. It was relaunched in April survey the southern section from Rodez Cathedral (Fig. 1795 and Méchain was supposed to return to Paris. 4) to Montjuïc (Mont-Jouy) Fortress near Barcelona (Fig. However, he feared for his life as many scientists had 5), which had been measured less accurately as 333 km been guillotined during the French Revolution. There- in length (URL3, URL14). fore, he travelled to Marseille and Perpignan at the end MéchaintravelledtoBarcelonainJune1792,wherehe of August to resume measurement. Weather conditions set up triangulation points in Catalonia during the sum- were very poor, but Méchain continued to refuse to re- mer. He measured angles using a repeating circle in autu- turn to Paris and meet Delambre, who had finished mn, and measured the latitude by astronomical methods measuring the trigonometric network in the northern in Barcelona very carefully during the three months of section and had not measured anything for two years, as winter. Thanks to cooperation from the Spanish, he was he had been incarcerated several times during the re- allowed to survey from the top of Montjuïc Fortress. volution. Although Delambre sent Méchain all his meas- When war broke out in March 1793 between France urement data, Méchain refused to reciprocate. He was and Spain, Méchain had to leave Montjuïc (485 m above afraid that his measurement error would be discovered sea-level) due to its military purpose. After being in- if he returned to Paris. So he started altering his data, jured while testing a hydraulic pump, he returned to the taking care that deviations were minimal. upper Pyrenees. However, he was still unable to return Méchain believed that accuracy could be achieved to Montjuïc because of war, so he measured the latitude with a repeating circle. He did not understand statistics from a hotel in Barcelona. By March 1794, Méchain had based on the random error theory, which had not yet connected this two points (Montjuïc – hotel) by terrest- been developed.
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